Bubbles and their flow dynamics strongly impact the performance of gas-evolving electrochemical systems with porous electrode architectures. The presence of bubbles on the electrode surface reduces the number of active catalytic sites that are accessible for the liquid electrolyte, leading to limitations in mass transport and/or reaction kinetics. Additionally, bubbles can obstruct the flow of liquid electrolyte that is able to pass through the porous structure, leading to pressure buildup. Therefore, to mitigate bubble blockage, optimal electrolyzer performance requires understanding bubble dynamics within the porous electrode in the presence of an applied flow; an accurate and complete physical model of this setup is not yet available. Here, we present volume-of-fluid simulation results and a theoretical framework to describe the bubble/electrolyte/electrode interaction, i.e. the triple phase boundary, ultimately with an aim to predict whether the bubble does or does not break through the porous media. Informed by the numerical results, the constructed theory describes the interaction of buoyancy, surface tension, and pressure drop for the range of different porosities, bubble sizes, and electrolyte flow rates. Comparison of these results with experimental findings are discussed. This work serves as a first step in building the framework for the design and optimization of relevant porous media systems that aim towards the improved control of bubble dynamics.This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL release number: LLNL-ABS-857509.